I haven't found any questions similar to this and am looking for some help. How should I go about representing a sentence similar to this in first order logic? I am not looking for someone to solve my homework, just looking for some guidance.
A sale is final only if the bill of sale has been approved by a Judge, a police officer, or a lawyer.
The following is my attempt:
$$ \forall x(J(x) \lor P(x) \lor L(x) \rightarrow \operatorname{Final}(x)).$$
Any suggestions are appreciated.
"Only if" is actually the opposite implication (think of "if and only if").
So in your case, "the sale is final only if approved by xyz" means that "if the sale is final then it has been approved by xyz".